Although the shortest-term quarterly interest rates for eurodollar futures begin each day at or near the rate dictated by the London Interbank Offered Rate (Libor), the rest of the eurodollar futures’ 40 quarters quickly adjusts to approximate the forward rates needed to generate the U. S. Treasury yield curve.

The actual relationship between eurodollar rates and U.S. Treasury yields shifts over time, in part because of changes in monetary policy by the Federal Reserve. The recent history of responses by eurodollar rates can be seen in a series of charts.

Before viewing the charts, however, we should define several terms: 1) rate is the interest rate specific to a single period, in this case one quarter of a year or three months—this is an interest rate for a 90-day maturity; 2) yield is the geometric mean of quarterly rates through a given maturity, so a five-year yield is equal to the geometric mean of the previous 20 quarterly rates, and 3) a forward rate has the same meaning as a quarterly rate and is specific for a given quarter. The required yield for any maturity implies the geometric mean of a series of forward rates leading up to that maturity, with the necessary structure of the shorter-term rates that will produce the yield.

The chain of 40 quarterly eurodollar rates may be converted into a yield curve by computing the geometric mean at the end of each quarter. Charts will show that the resulting eurodollar yield curve is an approximation of the U.S. Treasury yield curve unless Federal Reserve monetary policy causes a disruption in the normal pattern.

In the same way, only in reverse, the U.S. Treasury yield curve may be converted into a chain of previous quarterly forward rates by working backward through the geometric mean calculations. These are the rates that are mathematically required to generate the yield for a specific maturity.

Fed play

The U. S. Treasury yield curve is sometimes mistakenly seen as a forecast of future yields. As discussed, the yields for various maturities are a product of existing shorter-term rates and are simply “yields to maturity.” This also means that forward rates, as explained, are currently existing rates for specific quarters leading up to the yield and are the short-term rates that are required to produce the yield. The pattern, or maturity structure, of forward rates is dictated by the yield at the end of the chain of quarterly rates.

To see how Federal Reserve policy may affect the relationship between eurodollar futures rates or yields and U. S. Treasury yields, consider “Yields and rates: Feb. 1, 2007” (below). At that time, the Fed had instituted a tight-money policy in an attempt to slow what was perceived to be an overheated economy in the United States. The shortest-term interest rates were boosted to approximately 5.40%, while the yield curve sloped down to a 10-year yield of 4.80%. In other words, we had ourselves an inverted yield curve.

In response to the inverted yield curve in 2007, eurodollar rates also declined sharply from the shortest maturity through the two-year maturity, and then rose in a straight line slope through the remaining 32 quarters, from a low near 5% to a high of 5.80%. The eurodollar yield curve—the chain of geometric means that normally would approximate the U. S. Treasury yield curve—could not match the lower, inverted curve after the two-year maturity.

By the year following the 2007 inverted yield curve, interest rates and yields had decreased, with the shortest-term rates now lower than 3% and the 10-year U. S. Treasury yield slightly above 3%. “Yields and rates: March 17, 2008” (below) shows a more normal relationship between eurodollar rates and yields with the U. S. Treasury yield curve. The chain of eurodollar yields parallels the Treasury yields, with a difference of approximately 100 basis points after the two-year maturity.